This invention is in the field of symmetric cryptography. The field of cryptography is concerned with the diverse techniques that are used in facilitating the secure communication of confidential or proprietary information (messages) between two or more entities. Cryptographic techniques may be broadly divided into two categories—i) asymmetric cryptography or public-key cryptography, and ii) symmetric cryptography.
Classical symmetric cryptography is based on either permuting characters in a message or substituting one or more characters in a message with one or more characters from the same alphabet or different alphabets. The key associated with a particular algorithm dictates how the substitutions or transpositions are carried out. The key in the linear algebra-based Hill technique, for example, is an integer-valued matrix. [L. S. Hill. Cryptography in an algebraic alphabet. The American Mathematical Monthly. Vol. 36, pp. 306-312, 1929]. Modern cryptographic algorithms use both substitution and transposition of characters or groups of characters in a message, either directly or indirectly.
In public-key cryptography, the sender (say A) has two keys—a private key A keeps secret, and a public key which is made available to anyone (say B) who wishes to communicate with the sender. If B wishes to send a message to A, B uses A's public key to encrypt the message and A uses his/her private key to decrypt the message. Likewise, if A wishes to send a message to B, A uses B's public key to encrypt the message and send it to B; B then uses his/her private key to decrypt the message. The security of the [public-key, private-key] pair in asymmetric cryptography schemes is predicated on the inability of an intruder to compute the private key in a finite amount of time since key generation is based on obtaining the solution to computationally and mathematically hard problems. Examples of this include the Rivest-Shamir-Adelman (RSA) algorithm which is based on factoring the product of two very large prime numbers; the El Gamal cryptosystem which is based on solving the standard discrete logarithm problem and the Miller-Koblitz elliptic curve cryptographic technique which is based on solving the elliptic curve discrete logarithm problem. All of these techniques are centered on using integers, in particular large prime numbers.
In symmetric cryptography, both the sender and the recipient of a message use the same key in order to encrypt and decrypt the message. Since both the sender and the recipient share the same key, the key will need to be kept secret. However, in case the key falls into the wrong hands, any subsequent communications between the original sender and the intended recipient can be easily compromised. Well known modern symmetric cryptography algorithms include the Data Encryption Standard (DES) and the Advanced Encryption Standard (AES).
One way to prevent subsequent communications from being compromised is to make the key message-specific. Yet, if the key is poorly constructed, knowledge of a key from some prior communication can still be used to infer or partially construct a new key. It has been mathematically proven by Claude Shannon [C. E. Shannon. The synthesis of two-terminal switching circuits. Bell Systems Technical Journal, vol. 28, pp. 59-98, 1948] that the ‘one-time pad’ technique originally devised and patented by Gilbert Vernam [G. S. Vernam: Secret Signaling System. 1919. U.S. Pat. No. 1,310,719] is completely secure. In the Vernam method, the length of the key is the same as the length of the message and each character in a message is cyclically shifted a random number of positions. The KAFKA System described in this application is also a ‘one-time pad’ technique but it is significantly different from the Vernam technique. The significant differences are discussed in the section labeled ‘Detailed Description of the Invention’ under the heading ‘Points of particular interest’.